A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent γ moves with constant speed v on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be

Question

A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent &gamma; moves with constant speed v on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be (A) ((&gamma;-1) M v2/4 R) (B) (&gamma; M v2/2 R) (C) (M v2/2(&gamma;-1) R) (D) ((&gamma;-1) M v2/2 R)

Tardigrade Admin · Accepted Answer

Mass of gas in the box =2 M Initial kinetic energy =(1/2) × 2 M × v2=M v2 M v2=(1/2) n f R Δ T ∴ Δ T=(2 M v2/n f R) Substitution f=(2/1-r) and n=2 Δ T=((&gamma;-1) M v2/2 R)

Q. A box of negligible mass containing $2$ moles of an ideal gas of molar mass $M$ and adiabatic exponent $γ$ moves with constant speed $v$ on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be

$\frac{( γ - 1 ) M v ^{2}}{4 R}$

$\frac{γ M v ^{2}}{2 R}$

$\frac{M v ^{2}}{2 ( γ - 1 ) R}$

$\frac{( γ - 1 ) M v ^{2}}{2 R}$

Mass of gas in the box $= 2 M$
Initial kinetic energy $= \frac{1}{2} \times 2 M \times v^{2} = M v^{2}$
$M v^{2} = \frac{1}{2} n f R Δ T$
$∴ Δ T = \frac{2 M v ^{2}}{n f R}$
Substitution $f = \frac{2}{1 - r}$ and $n = 2$
$Δ T = \frac{( γ - 1 ) M v ^{2}}{2 R}$

Q. A box of negligible mass containing 2 moles of an ideal gas of molar mass M and adiabatic exponent γ moves with constant speed v on a smooth horizontal surface. If the box suddenly stops, then change in temperature of gas will be

4R(γ−1)Mv2​

2RγMv2​

2(γ−1)RMv2​

2R(γ−1)Mv2​